The discussion revolves around calculating the uncertainty in a squared quantity, specifically focusing on the expression D^2 derived from a measurement D with an associated uncertainty. The subject area includes uncertainty analysis in physics, particularly in the context of measurements and their propagation through mathematical operations.
Some participants have offered alternative formulas and approaches for calculating uncertainty, leading to a discussion about the accuracy of different methods. There is recognition of potential errors in the original poster's calculations, and some participants express understanding of the corrections provided.
Participants are working within the constraints of homework rules, which may limit the information they can share or the methods they can use. There is a noted confusion regarding the application of uncertainty formulas, particularly in the context of squaring a measurement.
gneill said:For the uncertainty as a result of a power in general, let Q = xn and δx be the uncertainty in x. Then
$$\frac{\delta Q}{|Q|} = |n| \frac{\delta x}{|x|}$$
In your case the power is n = 2 and x is a positive value, so that δQ becomes:
$$\delta Q = 2 x^2 \frac{\delta x}{x} = 2 x \delta x$$
Your formula A ((ΔA/A) + (ΔA/A) ) should have been A2 ((ΔA/A) + (ΔA/A) ).
NasuSama said:To make this problem simple, see D² as D * D.
Well, the rule for finding the uncertainty in multiplication is Δw = √((yΔx)² + (xΔy)²), coming from w = xy. It's the simpler similar version of the formula other user uses.
Now, you try to use that formula.